Adding Edge Loops to Meshes created with Skin
You are missing a step from the previous page. The first line reads -


  Once we have applied the Skin and Armature modifiers, we are left with an almost ready-to-use base mesh


You don't have the real mesh to add a loop cut because you haven't applied the skin and armature modifiers. Click the apply button on each modifier to get the mesh you can edit further.